Frequency Response of Servomechanisms with Non-linear Friction

Abstract

In this paper, the effect of non-linear friction, i.e. static and coulomb friction, on frequency response of the servomechanism, is considered in order to get the knowledge for synthesis of the servomechanism. The effect of non-linear friction does not depend on the absolute value of friction torque, but on the ratio of the static friction torque to the amplitude of sinusoidal input torque F/A. If the amplitude of sinusoidal input torque is not so large as the static friction torque, the output speed of the servomechanism has a dead zone in the low frequency range, and whether the output speed has a dead zone or not depends on the frequency of the sinusoidal input torque, the ratio F/A, and the other system parameters. The limiting condition of the output speed with a dead zone is considered. When the input torque varies sinusoidally, the waveforms of output speed of the servomechanism in which the non-linear friction characteristic is contained, are strictly analysed. From the results of the above analyses, the effect of non-linear friction on the frequency response of the servomechanism is discussed through the method of comparing the first harmonic component of the output speed with input torque. The magnitude of gain is less than that of the linear first order system and converges to a certain value determined by the characteristic of the non-linear friction in the low frequency range. The shape of gain curves is like the linear first order system and the curves approach the -20dB/decade line in the high frequency range. The break point frequency becomes a little larger than that of the linear first order system as F/A becomes larger. On the other hand, the phase angle delays more than that of the linear first order system in the low frequency range and less than that in the high frequency range. Moreover, the phase characteristic curves converge to a certain angle larger than -90°. So, in the high frequency range, the non-linear friction acts so as to stabilize the performance of the whole system.